Horosphere
Sign in to save220px|right|thumb|A horosphere within the Poincaré disk model tangent to the edges of a [[hexagonal tiling cell of a hexagonal tiling honeycomb]] thumb|Apollonian sphere packing can be seen as showing horospheres that are tangent to an outer sphere of a [[Poincaré disk model]] In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic n-space. It is the boundary of a horoball, the limit of a sequence of increasing balls sharing (on one side) a tangent hyperplane and its point of tangency. For n = 2 a horosphere is called a horocycle.
In the Vinony graph
Within Vinony's link graph, Horosphere is referenced by 28 other articles, and connects out to manifold, Poincaré disk model and vector bundle connection.
It is catalogued under topics including 3-manifolds, Curves and Hyperbolic geometry.
Its subject is documented across 6 Wikipedia language editions.
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Encyclopedic overview
4 sectionsContents
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220px|right|thumb|A horosphere within the Poincaré disk model tangent to the edges of a [[hexagonal tiling cell of a hexagonal tiling honeycomb]] thumb|Apollonian sphere packing can be seen as showing horospheres that are tangent to an outer sphere of a [[Poincaré disk model]] In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic n-space. It is the boundary of a horoball, the limit of a sequence of increasing balls sharing (on one side) a tangent hyperplane and its point of tangency. For n = 2 a horosphere is called a horocycle.
A horosphere can also be described as the limit of the hyperspheres that share a tangent hyperplane at a given point, as their radii go towards infinity. In Euclidean geometry, such a "hypersphere of infinite radius" would be a hyperplane, but in hyperbolic geometry it is a horosphere (a curved surface).
Excerpted from Wikipedia’s “Horosphere” article, available under the CC BY-SA 4.0 licence.